Stylized Properties of the Interest Rate Term Structure under the Benchmark Approach

Market models, which reflect stylized properties of the interest rate term structure, are widely used for modeling and pricing interest rate derivatives. We consider a market model involving the short rate and a global stock portfolio. We illustrate the stylized properties of the interest rate term structure implied by a system of stochastic differential equations specifying the short rate and the discounted stock index under the benchmark approach. Comparison with empirical evidence, particularly 10- and 30-year treasury bond yields, demonstrates the explanatory power of a discounted stock index modeled by a squared Bessel process. This paper discusses how models of the short rate and discounted stock index clarify the shape of the yield curve. It finds that a discounted stock index modeled by a squared Bessel process explains 10- and 30-year treasury bond yields effectively. The results help practitioners estimate long-term bond yields for valuing pension and life insurance liabilities, reducing required reserves. The study shows these models capture features like an upward-sloping yield curve and swap rate volatility hump, providing empirical support for using a squared Bessel process for long-term bond yields. Its originality is in applying the benchmark approach and comparing model outcomes with observed data.